The St. Thomas Winery plans to open a new production facility in Napa Valley, Ca

Question

The St. Thomas Winery plans to open a new production facility in Napa Valley, California. Based on information provided by the accounting department, the company estimates total fixed costs (FC) of $250,000 per year and average variable costs of:

AVC = 10 + 0.01Q

where AVC is average variable cost (in dollars) and Q is output measured in cases of output per year.

Questions:

a. Determine the firm%u2019s total variable cost function, TVC (HINT: Total variable cost can be determined as AVC x Q).

b. Determine the firm%u2019s total cost function (TC).

c. Estimate total cost (TC) and average total cost (ATC) for the coming year at a projected volume of Q = 4,000 cases.

d. St. Thomas Winery sells its product in a perfectly competitive market where the market-determined price is $110 per case.

i. How many cases (Q) should the firm produce and supply in order to maximize its total profit?

ii. Should the firm shut down or continue to produce? Why or why not?

e. An increase in worker productivity because of greater experience or learning during the course of the year resulted in a substantial cost saving for the company. Estimate the effect of learning on average total cost (ATC) if actual total cost was $522,500 at an actual volume of 5,000 cases.

Explanation / Answer

(a) TVC = 10Q + 0.01(Q^2)

(b) TC = 250,000 + 10Q + 0.01(Q^2)

(c) TC = 250,000 + 10*4000 + 0.01(4000^2) = 450,000

ATC = 450,000/4000 = 112.5

(d)(i) Total profit = 110Q - 250,000 - 10Q - 0.01(Q^2) = 100Q - 0.01(Q^2) - 250,000

Differentiating this and equating to zero for maximum, we get 100-Q/50=0 or Q=5000

So the company has to make 5000 cases

(d)(ii) At 5,000 cases, the ATC is 110 which is the same as the selling price of 110. So the company is neutral to continuing to produce or shutting down. However assuming there is no salvage value and the fixed costs continue, then the company should continue to produce to cover its fixed costs.

(e) Without learning the ATC is 550,000/5000 or 110. With learning, the ATC is 522,500/5000 or 104.5. So the difference is to the extent of 1-104.5/110 or 5%.

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