Intermediate Microeconomics 301 Problem Set # 2 Due Wednesday June 29, 2005

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1 Intermediate Microeconomics 301 Problem Set # 2 Due Wednesday June 29, A new chemical cleaning solution is introduced to the market. Initially, demand is Q D = p p 2 and supply is Q S = p. Determine the equilibrium price and quantity. The government then decides that no more than 75 units of this product should be sold per period, and imposes a quota at this level. How does this quota affect the equilibrium price and quantity? Show the solution using a graph and calculate the numerical answer. 2. Using the formula of elasticity, if the equation for the demand for cups is Q = p 2p 2 What is the elasticity of demand when p = $5? and when p = $15? 1

2 3. Suppose demand for TV is estimated to be Q = p + 10p x - 2p z + 0.1m If p = 80, p x = 50, p z = 150, and m = 30, 000 Answer the following questions: a) What is the price elasticity of demand? b) What is the cross price elasticity with respect to commodity x? Give an example of what commodity x might be. c) What is the cross elasticity with respect to commodity z? Give an example of what commodity z might be. d) What is the income elasticity? 4. Suppose a tax on beans of $.05 per can is levied on firms. As a result of the tax, the equilibrium price increases from $0.20 to $0.22. What fraction of the incidence falls on consumers? On firms? (though not required, drawing a diagram is always helpful) Suppose the supply elasticity is 0.6. What must the demand elasticity be? 2

3 5. What is the effect of a $1 specific tax on equilibrium price and quantity if demand is perfectly elastic and supply is perfectly inelastic? What is the incidence on consumers? Explain. 6. The coconut oil demand function is given by Q d = 1, p p p + 0.2Y where p is the price of coconut oil in cents per pound, p p is the price of palm oil in cents per pound, and Y is the income of consumers. Calculate the income elasticity of demand for coconut oil. (if you do not have all the numbers necessary to calculate numerical answers, write your answers in terms of variables.) 7. Suppose that the demand function for apple cider is estimated to be Q = 100 p, where p is the price paid by consumers in cents per bottle and Q is the quantity demanded in hundreds of thousands of bottles per day. The supply curve for cider is estimated to be Q = ¼ *p. Calculate the equilibrium price for bottles of cider and the equilibrium quantity sold. Illustrate using a diagram. An environmental group suggests that the government impose a specific tax per bottled beverage of 20 cents, to be paid when consumers buy cider and to be used by the government to defray the costs of cleaning up bottle litter. Determine the effects of a 20 cent tax per bottle on the equilibrium price paid by consumers and on the equilibrium quantity sold. What price do the cider-producing firms receive? 3

4 8. Jane has a weekly income of $30, which she allocates between movies, at $6 per movie, and boxes of six packed soda, at $6 per box. Below is her total utility (TU) schedule for each good. (3 points) Movie ($6 per each) Soda ($6 per box) Quantity TU Quantity TU a) Suppose Jane chooses 4 movies and 1 box of soda. Does this satisfy her weekly budget constraint? Calculate the marginal utility of the last dollar spend on each good. b) Explain why this is not the combination that maximizes Ms. Taker s total utility subject to her budget constraint Pat s utility function is U = 5A B. The price of A is p a = 10, the price of B is p b = 5, and her income Y, is $200. What is her optimal consumption bundle? How much utility 6 2 does she receive from this bundle? If her utility function was U = 10A B, how would her consumption decision change? 4

5 10. What happens to the budget line if the government applies a specific tax of $1 per gallon on gasoline but does not tax other goods? What happens to the budget line of the tax applies only to purchases of gasoline in excess of 10 gallon per week? (it s sufficient to answer this question using the diagram) 11. Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S,T)=2ST. It costs Linda $50 to buy a new pair of shoes or to spend an evening out dancing. Assume that she has $500 to spend on clothing and dancing. a) What is the equation for her budget line? Draw it (with T on the vertical axis), and label the slope and intercepts. b) What is Linda s marginal rate of substitution? Explain. c) Solve mathematically for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line. 5