11.2 demand function for that input.Short-run changes in market price result in changes tothe firm's short-run profitability. These can be mea-sured graphically by changes in the size of producerIncreases in the price of an input will induce substitu-tion and output effects that cause the firm to reducehiring of that input.PROBLEMS11.1John's Lawn Mowing Service is a small business that acts as a price-taker (i.e., MR = P). The prevailing market price of lawnmowing is $20 per acre. John's costs are given bytotal cost = 0.1q² + 10g + 50,whereq = the number of acres John chooses to cut a day.a. How many acres should John choose to cut to maximize profit?b. Calculate John's maximum daily profit.c. Graph these results, and label John's supply curve.11.2Universal Widget produces high-quality widgets at its plant in Gulch, Nevada, for sale throughout the world. The cost functionfor total widget production (q) is given bytotal cost = 0.25q².Widgets are demanded only in Australia (where the demand curve is given by qA = 100 – 2PA) and Lapland (where thedemand curve is given by q1 = 100 – 4PL); thus, total demand equals q = qA + qı. If Universal Widget can control thequantities supplied to each market, how many should it sell in each location to maximize total profits? What price will becharged in each location?11.3The production function for a firm in the business of calculator assembly is given byq = 2Vi,where q denotes finished calculator output and I denotes hours of labor input. The firm is a price-taker both for calculators(which sell for P) and for workers (which can be hired at a wage rate of w per hour).a. What is the total cost function for this firm?b. What is the profit function for this firm?c. What is the supply function for assembled calculators [q(P, w)]?d. What is this firm's demand for labor function [I(P, w)]?e. Describe intuitively why these functions have the form they do.11.4The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviarsells for $30 per pound. In bad weather it sells for only $20 per pound. Caviar produced one week will not keep until the nextweek. A small caviar producer has a cost function given byChapter 11: Prof it Maximization 39C = 0.5q² + 59 + 100,where q is weekly caviar production. Production decisions must be made before the weather (and the price of caviar) is knowbut it is known that good weather and bad weather each occur with a probability of 0.5.a. How much caviar should this firm produce if it wishes to maximize the expected value of its profits?b. Suppose the owner of this firm has a utility function of the formutility = VT,where t is weekly profits. What is the expected utility associated with the output strategy defined in part (a)?c. Can this firm owner obtain a higher utility of profits by producing some output other than that specified in parts (a) ar(b)? Explain.d. Suppose this firm could predict next week's price but could not influence that price. What strategy would maximiexpected profits in this case? What would expected profits be?11.5The Acme Heavy Equipment School teaches students how to drive construction machinery. The number of students that tischool can educate per week is given by q = 10 min(k, 1)", where k is the number of backhoes the firm rents per week, I is tnumber of instructors hired each week, and y is a parameter indicating the returns to scale in this production function.

Question

11.2 demand function for that input.Short-run changes in market price result in changes tothe firm's short-run profitability. These can be mea-sured graphically by changes in the size of producerIncreases in the price of an input will induce substitu-tion and output effects that cause the firm to reducehiring of that input.PROBLEMS11.1John's Lawn Mowing Service is a small business that acts as a price-taker (i.e., MR = P). The prevailing market price of lawnmowing is $20 per acre. John's costs are given bytotal cost = 0.1q² + 10g + 50,whereq = the number of acres John chooses to cut a day.a. How many acres should John choose to cut to maximize profit?b. Calculate John's maximum daily profit.c. Graph these results, and label John's supply curve.11.2Universal Widget produces high-quality widgets at its plant in Gulch, Nevada, for sale throughout the world. The cost functionfor total widget production (q) is given bytotal cost = 0.25q².Widgets are demanded only in Australia (where the demand curve is given by qA = 100 – 2PA) and Lapland (where thedemand curve is given by q1 = 100 – 4PL); thus, total demand equals q = qA + qı. If Universal Widget can control thequantities supplied to each market, how many should it sell in each location to maximize total profits? What price will becharged in each location?11.3The production function for a firm in the business of calculator assembly is given byq = 2Vi,where q denotes finished calculator output and I denotes hours of labor input. The firm is a price-taker both for calculators(which sell for P) and for workers (which can be hired at a wage rate of w per hour).a. What is the total cost function for this firm?b. What is the profit function for this firm?c. What is the supply function for assembled calculators [q(P, w)]?d. What is this firm's demand for labor function [I(P, w)]?e. Describe intuitively why these functions have the form they do.11.4The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviarsells for $30 per pound. In bad weather it sells for only $20 per pound. Caviar produced one week will not keep until the nextweek. A small caviar producer has a cost function given byChapter 11: Prof it Maximization 39C = 0.5q² + 59 + 100,where q is weekly caviar production. Production decisions must be made before the weather (and the price of caviar) is knowbut it is known that good weather and bad weather each occur with a probability of 0.5.a. How much caviar should this firm produce if it wishes to maximize the expected value of its profits?b. Suppose the owner of this firm has a utility function of the formutility = VT,where t is weekly profits. What is the expected utility associated with the output strategy defined in part (a)?c. Can this firm owner obtain a higher utility of profits by producing some output other than that specified in parts (a) ar(b)? Explain.d. Suppose this firm could predict next week's price but could not influence that price. What strategy would maximiexpected profits in this case? What would expected profits be?11.5The Acme Heavy Equipment School teaches students how to drive construction machinery. The number of students that tischool can educate per week is given by q = 10 min(k, 1)&#34;, where k is the number of backhoes the firm rents per week, I is tnumber of instructors hired each week, and y is a parameter indicating the returns to scale in this production function.

Accepted Answer

11.2 The inverse demand functions of locations A and L are;…