Multiple Choice Questions for a Quick Review:
Question 1. A competitive firm
a. Is a price taker in both the output and the product markets.
b. Is a price taker in the output market but not the product market.
c. Is a price taker in the product market but not the output market.
d. Is not a price taker in either the product nor the output market.
Question 2. A production function is a mathematical statement that
a. Relates the level of output to the level of inputs used.
b. Expresses the relationship between the prices of factors of production and the level of output produced.
c. Expresses the relationship between the amount of inputs used and the prices of those inputs.
d. May have the property of increasing returns to scale or constant returns to scale, but not the property of decreasing returns to scale.
Question 3. Aggregate income in an economy is
a. Equal to the total number of dollars earned by workers.
b. Always equal to aggregate production in that economy.
c. Equivalent to the dollar amount of payments made to owners of capital.
d. Equal to the total number of dollars earned as profits by firm owners.
Question 4. Constant returns to scale occurs when
a. The production function is linearly homogenous.
b. The exponents of capital and labor in the production function sum to one.
c. A doubling of inputs results in a doubling of output.
d. All of the above.
Question 5. Firms should continue to hire labor up to that point where
a. The marginal product of labor is just greater than the market wage rate.
b. The market wage rate is just greater than the marginal product of labor.
c. The marginal product of labor for the last unit of labor is just equal to the real wage rate.
d. The marginal product of labor for the last unit of labor is just equal to the price of the output.
Question 6. According to Euler’s Theorem, total output is equal to the sum of all factor payments provided that
a. Each factor of production is paid a real wage equal to its marginal product.
b. The production function is linearly homogenous (that is, it has constant returns to scale).
c. Equal amounts of capital and labor are used.
d. (a) and (b)
d. All of the above.
Question 7. Which of the following transactions is not counted as investment in the national income accounts?
a. A homeowner purchases a new washer and dryer for their home.
b. A homeowner purchases a new computer for their children.
c. A museum purchases a painting by Van Gogh for $40 million.
d. A homeowner purchases a new home built during the current calendar year.
Question 8. Which of the following statements is true?
a. Total saving is equal to the sum of private saving plus public saving.
b. Public saving is equal to G – T.
c. Private saving is equal to Y – C – G.
d. Private saving is equal to Y – C – G – T.
Question 9. Which of the following statements is true? If national saving is not dependent upon the level of interest rate, then an increase in government spending holding everything else constant must
a. Increase the interest rate.
b. Decrease the interest rate.
c. Reduce the budget deficit.
d. Increase the level of private investment.
Question 10. Which of the following statements is true? If national saving is not dependent upon the level of interest rate, then a decrease in taxes holding everything else constant must
a. Increase the interest rate.
b. Decrease the interest rate.
c. Have no effect on the interest rate.
d. May increase or decrease the interest rate depending upon how businesses alter their investment spending in response to the decrease in taxes.
Question 11. If the consumption function is C = 100 + .5(Y – T) then if disposable income decreases by $500 then consumption will
a. Increase by $250.
b. Decrease by $500.
c. Increase by $500.
d. Decrease by $250.
Question 12. If the consumption function is C = 100 + .5(Y – T) and Y = $4000 and T = $500 then the marginal propensity to consumer equals
a. $1750
b. $1850
c. .5
d. $2000
Question 13. A Cobb-Douglas production function
a. Exhibits constant returns to scale.
b. Is a production function that has a constant ratio of labor income to capital income.
c. Exhibits diminishing marginal productivity of labor.
d. Exhibits diminishing marginal productivity of capital.
e. All of the above.
Problems:
Q1. Suppose you operate a firm with a fixed amount of capital (K), 4 units, where capital costs $10/unit. In addition to the capital you use, you also employ labor (L). You also know the relationship between the factors you employ and the output (Y) you produce can be summarized in the following equation:
Y = F (K, L) = A K1/2L1/2
where A has a value of 2. You also know that the output produced by this competitive firm is sold for $10 per unit and that the nominal wage is equal to $10.
a. Fill in the table below:
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# of Workers
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Units of Output
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Marginal Product of Labor (approximation using the change in output divided by the change in labor
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Marginal Product of Labor (calculate using calculus)
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Nominal Wage
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Real Wage
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1
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x
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x
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2
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3
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4
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5
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9
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16
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25
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36
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b. Graph this firm’s production function. Make sure you label the axes in your graph.
c. Draw a second graph beneath your first graph and label the horizontal axis with the same units as the horizontal axis from the first graph. On this second graph plot out the firm’s marginal product of labor. Label the vertical axis appropriately.
d. Does this firm experience diminishing marginal product of labor as it expands its use of labor?
e. What level of labor should this firm employ? And what is the real wage rate at this level of production?
f. Why should this firm not hire 16 workers? Explain your answer.
g. Why should this firm not hire 2 workers? Explain your answer.
h. What happens to the firm’s demand for labor if the product price increases, holding everything else constant?
i. What happens to the firm’s demand for labor if the nominal wage rate decrease, holding everything else constant?
j. What happens to the firm’s demand for labor if the value of A increases, holding everything else constant?
Q2. Suppose you have a Cobb-Douglas production function described by the equation below:
Y = 5K1/4L3/4
a. Complete the following table:
Capital (K) Labor (L) Output (Y)
100 25
200 50
300 75
400 100
b. Does this production function exhibit constant returns to scale (allow for rounding error)?
c. Can you provide a mathematical proof of this based on the lecture material?
d. If this firm decides to hire 50 workers, what must the value of the real wage equal?
e. If this firm decides to hire 200 units of capital, what must the value of the real rental price of capital equal?
f. If this firm hires 50 workers and 200 units of capital, what is labor’s share of output?
g. If this firm hires 50 workers and 200 units of capital, what is capital’s share of output?
h. Does this sum of the value you found in (f) and the value you found in (g) sum to the value of output (allow for rounding error)?
Q3. Suppose you are given a consumption function
C = 100 + .8(Y – T)
a. Complete the following table.
Y T Y-T C
$0 $20
$100 $20
$200 $20
$500 $20
$1000 $20
$2000 $20
$5000 $20
b. Is the given consumption function a linear function with respect to disposable income? Explain your answer.
c. What is the marginal propensity to save? Provide a mathematical proof for your answer.
d. What does the slope of the consumption function tell you?
Q4. Suppose that there are two factors of production, K and L, that are fully employed in the economy we are studying. The following production function describes this closed economy which is operating at full employment.
Y = constant Y = F(K, L) = $1000
In addition to this information you know that:
• Consumption spending equals $100 when disposable income is zero and that the marginal propensity to consume is equal to .75.
• Investment is an inverse function of the interest rate (r) and that when the interest rate increases by 1 percentage point investment falls by $20.
• Investment is equal to $400 when the interest rate is zero.
• Government spending is constant at $100.
• Taxes are constant at $50.
a. What is the level of consumption in this economy?
b. What is the level of private saving in this economy?
c. What is the level of public saving in this economy?
d. What is the level of national (public plus private) saving in this economy?
e. Write an equation expressing the investment function for this economy.
f. What is the value of investment for this economy in equilibrium?
g. What must the equilibrium interest rate by for this economy?
Q5. Use the economy described in problem (4) to answer this question.
a. Suppose government spending increases to $150. What will be the effect of this change on this economy? Explain your answer.
b. How does a graph of saving and investment change with the events described in (a)?
c. Now, instead of events described in (a), suppose the government increased taxes to $100. What will be the effect of this change on this economy? Explain your answer.
d. How does a graph of saving and investment change with the events described in (c)?
e. Does fiscal policy have the potential to alter the level of aggregate output in the Classical Model?
f. What would happen in this model if there was a exogenous change in investment demand (assume we are back with the initial model: no changes in G or T) such that investment is now $50 more at every interest rate?
g. How does a graph of saving and investment change with the events described in (f)?