a.) Isolate the substitution and income effects graphically for good Y using the above graph. Identify each effect clearly on the Y axis.

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1 UNIVERSITY OF PUERTO RICO DEPARTMENT OF BUSINESS ADMINISTRATION GRADUATE DIVISION MANAGERIAL ECONOMICS, (ECOG 6567) FIRST MIDTERM EXAM Prof. Jimmy Torrez, Ph.D. You have an hour and twenty minutes to complete the Exam. Show your work. Y Y1 Substitution Effect Income Effect Y2 X 1.) Consider the above graph. The consumer has a choice of two goods X and Y. The decrease in the demand for Y from Y1 to Y2 represents a price increase in Y of approximately 200%. a.) Isolate the substitution and income effects graphically for good Y using the above graph. Identify each effect clearly on the Y axis.

2 b.) Explain each step in part a and why that step was necessary to isolate the two effects. First we need to make the consumer as well off after the price change as before the price change. We do this by shifting the new budget curve out until it is tangent to the old indifference curve. This is equivalent to giving the consumer enough money to make him as well off before the price change as after the price change. The change in the amount of Y after we make him as well off as before is known as the substitution effect. The substitution effect therefore measures the change in the product consumed cause solely by the change in price and not the fact that his real income has decreased. The remaining change from Y1 to Y2 is known as the income effect and is caused as a result of the consumer being able to buy less of the product because his real income has decreased. c.) Briefly explain why Economists believe it is important to isolate the substitution and income effects. Economist believe it is important to isolate the income and substitution effect because this can help determine how consumers will react to price changes and how the will react to income changes. It can also help us determine what the affect on demand will be when there is a simultaneous change in prices and income. It can also aid policy makers determine welfare losses due to tax increases on products. 2) Last week, Discount Food Stores, Inc. reduced the average price on the 22 once size of Dishwashing Liquid by 1%. In response, sales jumped by 8%. A. Calculate the point price elasticity of demand for Dishwashing Liquid. (% Q/% P)=(8%)/(-1%)= -8 B. Calculate the optimal price for Dishwashing Liquid if marginal cost (MC) is 70 per unit. (Hint. MR=P(1+(1/ p))= P(1-(1/ p )), Where MR=marginal revenue and p is point price elasticity of demand).

3 At the optimal level of consumption MC=MR so MC=MR=P(1+(1/ p)) MR=.70=P(1+(1/(-8))=P(7/8) P=.70/(7/8)=.70*(8/7)=.80 3.) Thomas Magnum, financial analyst for Detroit Wheels, Inc. has hired you to analyze demand in 20 regional markets for Product Y, a major item. A regression analysis of demand in these markets shows the following (standard errors in parentheses). QY = 85,000-1,000P PX A I (110,000) (600) (180) (0.4) (0.1) R 2 = 0.95 Standard Error of the Regression = 10 Here QY is market demand for Product Y, P is the price of Y in dollars, A is dollars of advertising expenditures, PX is the average price in dollars of product X, and I is dollars of

4 household income. In a typical market, the price of Y is $100, PX is $75, advertising expenditures are $50,000 and average family income is $42,500 a. Use the estimated demand function to calculate the expected value of QY in a typical market. QY = 85,000-1,000(100) (75)+ 0.05(50,000) (42,500) QY =7100 b. How much of the variation in demand for product Y does this demand estimation explain? The R 2 is a measure of how much variation in the dependent variable can be explained by the independent variables. Therefore since R 2 =.95 the variation in demand explained by this demand estimation is 95%. c. Which of the above coefficients (including the intercept) is statistically significant at the 90% level of significance using a 2-tailed test? (Hint: The t-statistic is the coefficient divided by the standard error of the coefficient. The t-distribution cutoff for a 2-tailed test at the 90% level of significance is ) t-statistic(coefficient/s.e.e.) intercept 85,000/110,000=.77 P 1,000/600= 1.67 Px 250/180=1.39 A 0.05/0.4= I 0.02/0.1=.2 To determine whether a variable is significant at a certain probability level the t-statistic must be greater than the cutoff for the level of probability. In this case the cutoff for a 90% level of

5 significance is The only coefficient that has a t-statistic greater than the cutoff of is P (Price). d. Calculate the point price elasticity of demand. Elasticity of demand can be written as follows (% Q/% P). This question asks for point price elasticity. Which can be written as (% Q/% P)= ( Q/ P)*(P/Q) Since for every unit price in P, Q decrease by 1000, ( Q/ P)=1000 p =( Q/ P)*P/Q=1000*(100/7100)=14.08 Alternatively we can assume that price increases by 10% (or any percentage change) and then calculate how much Q changes in percentage terms. In this case a 10% change in price equal to $10. Therefore Q will decrease by Q =1000(10)=10000 which means that ( Q/ P)=10000/10=1000 p =( Q/ P)*(P/Q)=100*(100/7100)=14.08