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Suppose that the utility function of a typical visitor to an amusement park is U (r,...

Question:

Suppose that the utility function of a typical visitor to an amusement park is U (r, y) = r - (1/2)p2 + y, where r is the num

Suppose that the utility function of a typical visitor to an amusement park is U (r, y) = r - (1/2)p2 + y, where r is the number of rides and y is expenditure on all other goods. The current price per ride is p. Each visitor has income of M. The MU, = 1-r. (a) Derive the Marshallian or ordinary demand function for rides. Com- ment the demand function. (b) On a diagram, graph the visitor's optimal number of rides and con- sumption of other goods for three different income levels that is con- sistent with your result from part a). (c) Find the Hickisan demand function for rides. How it is related to that you found in a)? Why? (d) Show that consumer surplus is CS(p) = (1 – p)2 /2. What happens to surplus as p increases? (e) Show that consumer surplus is equivalent to the increase in utility at the optimal choice for r relative to r = 0. (f) Find the compensating variation, the maximum that the visitor would be willing to pay, for entrance into the park. Entrance gives them the right to go on as many rides as they would like for price r per ride. (g) Find the maximum they would be willing to pay to lower the price from $0.50 per ride to $0.25 per ride. Show this in a graph with indif- ference curves and in another graph with the demand curve. (h) How much would they have to be compensated if the price of rides did not fall?

Answers

Q.1, ulvy) = 9 -(+)*ty, yas zincome spact on the goals a, now at eam. MRd.ry =P MUY S MUU Mes normes 4-44)-2x = 1-1 &.at eqm,

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