02 Jun Question 1. Angela derives utility from Coca-Cola (C) and at
Question
1. Angela derives utility from Coca-Cola (C) and attending rock concerts (R). Her utility function is U(R,C) = C0.9R
0.1, where C and R are the number of colas and rock concerts consumed per year, respectively.
A. If the price of colas is $1 and the price of concert tickets is $30, and Angela’s income is $300, how many colas and concert tickets will she buy to maximize utility? Verify that MRS = MRT at the optimal solution.
B. Suppose the promoters of the rock concert make the following requirement: Either buy four rock concert tickets or none at all. Under this constraint, and given the prices and income above, how many colas and rock concerts will Angela buy to maximize utility? Verify that MRS ? MRT at the optimal solution.
2. The market demand for laptops (good X) is given by:
QX
D
= 1,200 – 0.4PX
1/2
– 4PY
1/2
+ 5I + AX
Where QX
D is the quantity demanded of laptops, PX is the price of a laptop, PY is the price of a smartphone, I is income, and AX is advertising expenditures on laptops. Suppose we know that PX is 200, PY is 40, I is 150, and AX is 10.
A. Answer the following (using the demand determinant coefficients and calculus)
(i) Is the law of demand satisfied?
(ii) Are X and Y complements or substitutes?
(iii) Is X a normal or inferior good?
(iv) Is Y a normal or inferior good?
B. Calculate a demand elasticity for each demand determinant.
C. Are laptops a luxury or a necessity?
D. Based on your elasticity value in Part B, would you characterize the advertising program as effective or not? Would you suggest that further advertising be undertaken?
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