Professor Glasure ECON 3315 Problem Set #4 Production 1. Optimal Use of a Single Input. Julian Smyth is manages production at Taffy Apple Inc., a...

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Professor Glasure ECON 3315Problem Set #4Production 1. Optimal Use of a Single Input. Julian Smyth is manages production at TaffyApple Inc., a company that produces a variety of taffy/fruit candies. Over thelast several months, he has varied then number of employees on his caramelapple production line, and found the following relationship.Labor56789101112 TP100150230300360410450480 MP MRP 50807060504030 250400350300250200150 a. In the column labeled MP, calculate the marginal product of labor. (Note,make your first entry in row 6, as the change between 5 and 6 units of labor)b. Suppose the apples sell for $5 (per dozen) box. Calculate the MarginalRevenue Product (MRP) c. If labor costs $225 per day, how many laborers should the firm hire?Number ___________________________________________ 2. Optimal Use of a Single Input. A graphical representation.a. In the coordinate axes provided below, illustrate the general relationshipbetween MRP and the Price of Labor. Identify the equilibrium quantity oflabor to hire. (Note, your graph need not use the numbers in problem 3.Just be certain to include ranges that illustrate gains from specializationand the law of diminishing returns in your graph.$ Qb. Suppose that the candy workers union agrees to way concessions, thatmake the price of labor fall. In the coordinate axes below illustrate theeffect on the equilibrium quantity of labor $ Qc. Finally, suppose that the price of caramel apples increases. Illustrate theeffect of this change on the equilibrium quantity of labor employed.$ Q 3. Optimal use of multiple inputs. In his shop, Julian Valenti retrofits sunroofsinto automobiles. The process can use a combination of skilled labor andunskilled labor. Given his current mix of employees, the marginal product of thelast unit of skilled labor is 3 sunroofs per day, and the marginal product of thelast unit of unskilled labor is 1 sunroof per day. Current market rates for skilledand unskilled labor are $40 and $10, respectively. Is Julian using a least costcombination of inputs? If not, which of type of labor should he use relativelymore?Comparison Expression:_______________________________________Result:______________________________________________________ 4. Returns to Scale. Jake’s Free Runoff Bottled Water Company Produces with theLong Run Production FunctionQ = (KL)2/3a. Currently K = 4 and L = 4. If Jake’s doubles inputs to K=8 and L=8, will it realizeincreasing, constant or decreasing returns to scale (circle one)? b. As a result, does Jake’s enjoyeconomies of scale, diseconomies of scale, or does Jake’s appear t be operating at Efficient Scale? (circle one)