Question

The Philadelphia Phillies occasionally offer “Dollar Dog Nights” as a way to promote attendance at ballgames (baseball games routinely do not sell out). Suppose they sell hot dogs for $1 each and chili dogs for $3 each. Dan attends the game and has utility such that U = √? +√?. Dan only has $15 cash and no credit card. a. Draw a sketch of an indifference curve so that all bundles on the curve provide U=10. Let qH be on the horizontal axis. b. What is Dan’s marginal utility from consuming additional hot dogs (UH) and chili dogs (UC)? c. What is Dan’s marginal rate of substitution between hot dogs and chili dogs in terms of H and C? d. Write an expression for the budget line and find the marginal rate of transformation along the budget line. e. Determine Dan’s utility maximizing bundle given the above utility function, budget, and prices. Feel free to use any method you are comfortable with so long as you characterize the utility optimizing bundle, so show your work. f. Suppose the Phillies decide to raise the price of hot dogs to $1.50 and the price of chili dogs to $4. Also, Dan finds an additional $20 in his pocket, bringing his total available cash to $35. Find Dan’s new optimal consumption bundle of hot dogs and chili dogs.

Answer 1

(a) The indifference curve, which provides U = 10 can be sketched as follows: