Find the market demand for ice cream if travis and maya are

Question

1. The figure below illustrates the best feasible bundle of steak, x, and rice, y, for an individual given current income and prices. The budget line is labeled A and the bundle is labeled a.

a. Illustrate how an increase in the price of steak (so the new budget line is B) changes the utility-maximizing bundle. Label the new one b. (You need to draw the 2nd indifference curve.)

b. Decompose the movement from a to b into substitution and income effects. Label the "halfway point" m.

c. Given the way you have drawn your figure, is steak a normal or inferior good?

d. Could an increase in the price of steak ever increase the quantity of steak demanded? Explain.

2. Travis' demand for ice cream is given by Q_T = 12 - 3P and Maya's is given by Q_M = 6 - P.

a. Find the market demand for ice cream if Travis and Maya are the only two consumers in the market. (Remember, Travis' demand at P = 5 isn't -3, it's 0!)

b. What is the price elasticity of demand when P = 2?

c. At this price, is demand elastic, unit elastic, or inelastic?

d. If this price were to increase slightly, what would happen to the total revenues from ice cream sales?

3. Suppose Bob has a utility function ??(??, ??) = ln(??) + y/4. Suppose the price of x is p_x = $2, the price of y is p_y = $1, and Bob's income is m = $8.

a. Show that the marginal rate of substitution as a function of x & y is x/4.

b. Set the MRS equal to the price ratio to find the income-consumption curve.

c. How many units of x and y will Bob buy?

d. Suppose the price of y increases to 2. How many units of x and y will Bob buy?

e. Suppose the price of y increases to 3. How many units of x and y will Bob buy?

f. Would your answers to parts a-e change if his utility function were ??(??, ??) = 4 ln(??) + ??? Why or why not?

4. For each case a, b, & c, sketch the following:

I. 3 or 4 budget lines (with the same p_x & p_y), and the indifference curves they are tangent to, with the income-consumption curve
II. Engel curve (quantity of x vs m)
III. 3 or 4 budget lines (with the same m & p_y), and the indifference curves they are tangent to, with the price-consumption curve
IV. Demand curve (quantity of x vs p_x)

a. x is a Normal good
b. x is an Inferior good (and not Giffen)
c. x is a Giffen good.