SOLUTION: Marginal Rate of Technical Substitution | My Assignment Tutor

1Managerial EconomicsTutorial Solutions – Week 4Hirschey 15th Edition: Chapter 7: Problems P7.1 and P7.7P7.1 Marginal Rate of Technical Substitution. The following production table gives estimates of themaximum amounts of output possible with different combinations of two input factors, X and Y.(Assume that these are just illustrative points on a spectrum of continuous input combinations.) Units ofY UsedEstimated Output per Day521030536042147041882723243764213162234282324360213018823427230519413016218821012345Units of X used A. Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates oftechnical substitution? How do you know?The inputs exhibit the characteristic of a decreasing marginal rate of technical substitution throughout.For decreasing MRTS, the slope of the production isoquants diminishes as one input is increasinglysubstituted for another. We can also see this point algebraically by holding X or Y constant in the inputoutput matrix and noting the decline in the relative marginal product of the other input as its usage levelgrows.B. Assuming that output sells for $3 per unit, complete the following tables: X Fixed at 2 UnitsUnits ofY UsedTotalProductof YMarginalProductof YAverageProductof YMarginalRevenueProductof Y12345 2 Y Fixed at 3 UnitsUnits ofX UsedTotalProductof XMarginalProductof XAverageProductof XMarginalRevenueProductof X12345 X Fixed at 2 UnitsUnits of YEmployedTPY(1)MPY(2)APY(3)MRPY(4) = $3 × (2)1130130130$3902188589417432344678138427238681145305336199Y Fixed at 3 UnitsUnits of XEmployedTPX(1)MPX(2)APX(3)MRPX(4) = $3 × (2)1162162162$486223472117216328248941444324428112653603672108 C. Assume that the quantity of X is fixed at 2 units. If output sells for $3 and the cost of Y is $120 perday, how many units of Y will be employed?Y = 3 will be employed. The marginal value of the first three units of Y is greater than their marginal cost.The marginal value of the fourth unit is only $114 or $6 less than its cost, and hence, the firm wouldemploy no more than 3 units of Y.3D. Assume that the company is currently producing 162 units of output per day using 1 unit of X and3 units of Y. The daily cost per unit of X is $120 and that of Y is also $120. Would you recommenda change in the present input combination? Why or why not?A change would be in order because the firm could produce 188 units at the same cost using 2 units ofeach output: that is, the marginal product to price ratios of the two inputs are not equal at the currentinput proportions. Relatively less Y, and more X, is needed to provide an optimal combination.E. What is the nature of the returns to scale for this production system if the optimal inputcombination requires that X = Y?The system exhibits constant returns to scale. This is true because a given increase in both inputs causesan increase in output of the same proportion. XYOutput1194 × 1 = 942294 × 2 = 1883394 × 3 = 2824494 × 4 = 3765594 × 5 = 470 P 7.7 Marginal Revenue Product of Labour. To better serve customers interested in buying cars overthe Internet, Smart Motors, Inc., hired Nora Jones to respond to customer inquiries, offer price quotes,and write orders for leads generated by the company=s web site. During last year, Jones averaged 1.5vehicle sales per week. On average, these vehicles sold for a retail price of $25,000 and brought thedealership a profit contribution of $1,000 each.A. Estimate Jones’ annual (50 workweek) marginal revenue product.In the long run, Jones’ marginal revenue product is the maximum amount Smart Motors could pay inbase salary plus all fringe benefits. It is the amount of added revenue after all other variable costs thatJones’ effort brings to the firm. In this case, Jones’ marginal revenue product is determined by thenumber of cars sold and the profit contribution earned on each sale.MRPL = MPL X MRQ= (Car sales per year) X (Profit contribution per unit)= (1.5 X 50) X ($1,000)= $75,000Because Jones is only engaged in the sales function, Jones does not produce cars. What Jones doesproduce are car sales, and the added value to the employer of Jones’ sales effort is what determines theamount the employer is willing and able to pay.4B. Jones earns a base salary of $60,000 per year, and Smart Motors pays an additional 28% of thisbase salary in taxes and various fringe benefits. Is Jones a profitable employee?No. In addition to base salary, employers must pay additional taxes and fringe benefits. All of these costsmust be justified by the amount of marginal revenue product generated to justify employment. In thiscase, employment costs for Jones are $76,800 (= $60,000 X 1.28). A comparison of marginal revenueproduct figures with these employment cost data suggests:MRPL = $75,000