Problems to learn:
Question 1: Before Sam quit his job as a hairdresser, he was earning $34,000 per year. He rented an office for $18,000 per year and opened a framing shop. He spends $88,000 per year for labor, materials, utilities, and advertising.
(A). How much revenue will the business have to earn in order to break even in terms of business profit?
(B). How much revenue will the business have to earn in order to break even in economic terms?
(C). Suppose that Sam buys the building. How will this influence the amount that the business will have to earn in order to break even in economic terms? In accounting terms?
Question 2: Q2: Assume that the demand is represented by the following equation:
QD = 100 + 0.01 Income - 3P
Also assume that the supply is represented by the following equation:
Q5 = P - 10
(A) Assume that the consumer income is $3,000. Please compute the market equilibrium price and quantity.
(B) Now, assume that the economy goes into a recession and the consumer's income declines to $2,000. What will the new equilibrium values be now?
Question 3: Jane spends $210 per month on wine and beer. Her utility function is given by
TU = 100WB, where W represents the number of bottles of wine that she buys and B represents the number of cases of beer that she buys. If wine costs $10 per bottle and beer costs $15 per case, what is the optimal combination of wine and beer she will consume to maximize her utility?
Question 4: A firm's demand function is Q = 16 - Pand its total cost function is defined asTC = 3 + Q + 0.25Q2. Use these two functions to form the firm's profit function and then determine the level of output that yields the profit maximum. What is the level of profit at the optimum?
Question 5: The price of a good increases from $8 to $10, and as a result the quantity of the good demanded declines from 120 to 80. Calculate the price elasticity of demand using the arc formula and determine whether demand is elastic, inelastic, or unit elastic.
Question 6: Use the total cost (TC) schedule that is presented in the table below to calculate average total cost, total fixed cost (TFC), total variable cost (TVC), average variable cost (AVC), average fixed cost (AFC), and marginal cost (MC).
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Q
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TC
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TFC
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TVC
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ATC
|
AFC
|
MC
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0
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3
|
|
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-----
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-----
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-----
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1
|
6
|
|
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2
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8
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|
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|
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3
|
11
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|
|
|
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|
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4
|
15
|
|
|
|
|
|
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5
|
20
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|
|
|
|
|
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6
|
26
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|
|
|
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|
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7
|
34
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|
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8
|
55
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|
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9
|
70
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|
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|
Question 7: A firm has estimated the following demand function for its product:
Q = 8 - 2P + 0.10I + A
where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month in thousands. Assume that P = $10, I = 120, and A = 10. Use the point formulas to complete the elasticity calculations indicated below.
(A) Calculate quantity demanded.
(B) Calculate the price elasticity of demand. Is demand elastic, inelastic, or unit elastic?
(C) Calculate the income elasticity of demand. Is the good normal or inferior? Is it a necessity or a luxury?
(D) Calculate the advertising elasticity of demand.
Question 8: The table below shows annual demand (in 100,000 units per year) for Smidgets (they're like Widgets, only smaller). Use this information to calculate a linear trend forecasting model using regression analysis. Use your trend estimate to forecast demand for the years 1996 and 2001.
Year Demand
1990 2
1991 4
1992 5
1993 9
Question 9: The table below shows semi-annual demand (in thousands) for Shidgets (they're like Widgets, only quieter). A linear trend has been estimated using this data set with t = 1 for 1990.1 and t = 8 for 1993.2. It has an intercept of 0.76 and a slope of 0.20. Use the ratio-to-trend method to calculate seasonal adjustment factors for the first and second half of the year and then forecast the level of demand for 1995.1 and 1995.2. Note: Round all intermediate calculations to two decimal places.
Year Demand
1990.1 1.0
1990.2 1.1
1991.1 1.4
1991.2 1.5
1992.1 1.8
1992.2 1.9
1993.1 2.3
1993.2 2.3
Question 10: City government has collected the following data on annual sales tax collections and new car registrations:
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Y: Annual Sales Tax Collections ($ millions)
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X: New Car Registrations(thousands)
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1.0
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10
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1.4
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12
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1.9
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15
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2.0
|
16
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2.1
|
17
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2.3
|
20
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(A) Determine the least squares regression equation.
(B) Predict the total sales if the new car registration is 19 thousand.