Gerald operates an automobile detailing business in Mombasa City. An automobile retailer restores a car to the level of cleanliness and perfection that it had when it was new. His fastidious nature, attention to detail and ability to effectively manage employees have helped to make his business profitable, but he believes that more information about the market would allow him to operate more efficiently. He uses regression analysis to estimate the demand function for his business and gets the following result:

Q_X = 235 - 3P_X + 40_A - 20_U + 8P_W

The number of detailing jobs he gets per month (Q_X) depends on the price he charges per job (P_X), his monthly advertising expenditures (A) measured in Shs 1,000s, the regional percentage unemployment rate (U), and the average price charged by local car wash businesses (P_W) for a standard wash and wax.

Use the estimated demand function given to solve the following questions

(i)Is automobile detailing a normal good or an inferior good? How can you tell?

(ii) Is a wash and wax at the local car wash a complement or a substitute for automobiledetailing? How can you tell?

(iii) Gerald is currently charging shs 65 per detailing job and spending shs 3,500 per month on advertising. The regional unemployment rate is 7.5% and the average price of a wash and wax at a local car wash is shs 15. How many detailing jobs per month can Gerald expect under these conditions? Derive the demand curve for detailing jobs under current conditions.

(iv) Calculate the point advertising elasticity of demand (%QX/%A) under current conditions. Is it elastic or inelastic?

(v) How many additional detailing jobs would result if Gerald spent an additional shsh1,000 on advertising? How much additional revenue will be generated, under current conditions, if an additional shs 1,000 is spent on advertising? Assume that Gary increases his advertising expenditures to shs 4,500 while all other conditions remain unchanged.

The market demand and supply equations for a product are

Q_D=300-3P

Q_s = 100+5P

where Q is quantity and P is price.

(i) What are the equilibrium price and quantity for this product?

(ii) Suppose that an increase in consumer income resulted in the new demand equation

Q_D=420 - 3P

What are the new equilibrium price and quantity for this product?

(iii) Suppose the government enacts legislation that imposes a price ceiling equivalent to the original equilibrium price. What is the result of this legislation?

(iv) Discuss various ways the government influences the market equilibrium

(a) Lothian Company has estimated the following production function for its product

Q= 10 K ^0.3 L ^0.7 where Q represents units of output, K units of capital, and L units of labor.What is the coefficient of output elasticity? What are the returns to scale?

(b) Suppose that a firm's total cost equation is TC = 10,000 + 100Q+ 25Q² where TC is total cost and Q is the level of output.

(i) What output level will minimize the firm's average total cost?

(ii) Calculate the average and marginal cost at the average cost minimizing output level.

Suppose that an investment opportunity, which requires an initial outlay of $100,000, is expected to yield a return of $250,000 after 30years.

(i) Will the investment be profitable if the cost of capital is 7%?

(ii) Will the investment be profitable if the cost of capital is 2%?

(iii) At what cost of capital will the investor be indifferent to the investment?

It is not possible to have multiple Nash equilibria in the presence of a sub-game perfect equilibrium. Do you agree with this statement? If not, why not?