Can someone please help me with number 5 & 6 (NOT 1 - 4) with explanations? Laur
ID: 1158450 • Letter: C
Question
Can someone please help me with number 5 & 6 (NOT 1 - 4) with explanations?
Laura has been hired to help a struggling winery return to profitability. The winery produces wine using grapes (g) and labor (I). Wine sells at market price p, grapes are bought at cost r per pound of grapes and workers are paid a wage w per hour. The firm faces fixed cost F 1. The winery produces 400 bottles of wine per week and sells them at the market price of p - $30 per bottle. The winery's variable costs for producing wine amounts to S11,200 per week, and the winery must pay a weekly rent of F - $1,000 whether they produce wine or not. If the winery is maximizing profit, should they stay in business or shut down? Explain your answer. 2. If a potential entrant into the wine market is facing similar costs and market prices, should they rent land and enter the market? 3. Laura estimates the winery's production function to be y-6g1/311/3, and notes that the winery used 1000 pounds of grapes and 512 hours of labor per week last year. Was the winery's production efficient, or inefficient? Explain your answer. 4. Suppose grapes cost r $20 per pound and workers were paid w $10 per hour last year. Was the winery's combination of inputs last year profit maximizing? Explain your answer. 5. Was the production plan last year cost minimizing given the firm's output? Explain your answer. 6. If Laura gets the winery to produce efficiently and maximize profits, should they stay in business in the long run assuming prices and costs will remain exactly the same?Explanation / Answer
The winery produces 480 bottles of wine using y = 6(gl)^(1/3). Optimum usage of g = 1000 and l = 512. This gives y = 6*10*8 = 480 bottles. At wage rate = 10 and cost of grapes r = 20, the wage cost ratio is w/r = 10/20 = 0.5. MRTS = MPL/MPG = 6*(1/3)*g^(1/3)/l^(2/3) divided by 6*(1/3)*l^(1/3)/g^(2/3) which gives MRTS = g/l. Now g/l gives 1000/512 which turns to 1.95. Since MRTS > w/r the input mix is not cost minimizing.
In the short run the production is 400 bottles (part a) and MRTS = g/l At optimum input mix we have MRTS = w/r so that we have g/l = 10/20 which gives l = 2g. This becomes
400 = 6*(g*2g)^1/3 or
(400/6) = (2g^2)^1/3
This gives g = 384.90 and l = 769.80
Cost of production is 384.90*20 + 769.80*10 = $15396. Revenue is 400*30 = 12000. Since revenue is less than cost, the firm should leave in the long run.