In 1993, Broward County adopted both a licensing and a zoning ordinance for adult businesses.SeeBroward County, Fla., Ordinance 93-18 (July 13, 1993) (licensing); Broward County, Fla., Ordinance 93-3 (January 26, 1993) (zoning). The licensing ordinance (93-18) establishes detailed requirements for the physical structures of adult businesses, restricts the activities that can take place on the premises, and provides a licensing regime with application procedures and inspections. The zoning ordinance (93-3) merely modified Broward County's existing zoning regime for adult businesses, which this court found constitutional inInternational Eateries of Am. v. Broward County,941 F.2d 1157, 1165 (11th Cir.1991). Both the former and the new zoning ordinances require adult businesses to locate more than 500 feet from residentially zoned districts, and 1,000 feet from each other and from churches, schools, and child care facilities. The new ordinance eliminates a "waiver" provision that had allowed adult businesses to locate at a non-conforming site if the surrounding community approved. The former zoning ordinance also allowed existing businesses to remain on non-conforming sites, while the new 93-3 requires adult businesses to move to a conforming location within a five-year amortization period.

11.Let the consumer's utility function be (,,) = , and her budget constraint y = + + . Consider q₁ + (p₂/p₁)q₂ = q_c as a composite good. Formulate the consumer's optimization problems in terms of q_c and find the demand function for q_c.

12.A consumer who conforms to the von Neumann-Morgenstern axioms is faced with four situations A, B, C, and D. She prefers A to B, B to C, and C to D. Experimentation reveals that the consumer is indifferent between B and a lottery ticket with probabilities of 0.4 and 0.6 for A and D respectively, and that she is indifferent between C and a lottery ticket with probabilities of 0.2 and 0.8 for B and D respectively. Construct a set of von NeumannMorgenstern utility numbers for the four situations

13.A consumer who obeys the von Neumann-Morgenstern axioms and has an initial wealth of 160,000 is subject to a fire risk. There is a 5 percent probability of a major fire with a loss of 70,000 and a 5 percent probability of a disastrous fire with a loss of 120,000. Her utility function is U = ^.. She is offered an insurance policy with the deductibility provision that she bear the first 7620 of any fire loss. What is the maximum premium that she is willing to pay for this policy?

14.Determine the domain over which the production function q = 100(x₁ + x₂) + 20x₁x₂- 12.5( +

) is increasing and strictly concave.

15.Assume that an entrepreneur's short-run total cost function is C = + 17q + 66. Determine the output level at which he maximizes profit if p = 5. Compute the output elasticity of cost at this output.

16.An entrepreneur uses one input to produce two outputs subject to the production relation x

= A( + ) where , > . He buys the input and sells the outputs at fixed prices. Express his profit-maximizing outputs as functions of the prices. Prove that his production relation is strictly convex for q₁, q₂ > 0.

17.An entrepreneur uses two distinct production processes to produced two distinct goods, Q₁ and Q₂. The production function for each good is CES, and the entrepreneur obeys the equilibrium condition for each. Assume that Q₁ has a higher elasticity of substitution and a lower value for the parameter than Q₂. Determine the input price ratio at which the input use ratio would be the same for both goods. Which good would have the higher input ratio if the input price ratio were lower? Which would have the higher use ratio if the price ratio were higher?

18.Use Sherphard's lemma to find the production function that corresponds to the cost function

C = (r, and demonstrate that it is CE

19.A linear production function contains four activities for the production of one output using two inputs. The input requirements per unit output are

= = = = = = = =

20.Construct a short-run supply function for an entrepreneur whose short-run cost function is

C = 0.04 . + + .