Question #85307

Your company Must-Stash is the sole producer of the popular “I am awake and this is interesting” expression mask. The mask is a highly useful product for students everywhere.

(a) You are currently selling your product via a distributor. Your cost of production is TC(x) = 20x and the demand for the masks is given by D(P) = 50(30 – P), where P is the price to consumers. Assume the distributor’s costs are zero and you are charging your distributor a single price W per mask. What is the price W you charge your distributor? What price P do they charge the consumers and what is the quantity of masks produced and sold? What are your profits? Explain your calculations.

(a) You are currently selling your product via a distributor. Your cost of production is TC(x) = 20x and the demand for the masks is given by D(P) = 50(30 – P), where P is the price to consumers. Assume the distributor’s costs are zero and you are charging your distributor a single price W per mask. What is the price W you charge your distributor? What price P do they charge the consumers and what is the quantity of masks produced and sold? What are your profits? Explain your calculations.

Expert's answer

(a) TC(x) = 20x, D(P) = 50(30 – P) = 1500 - 50P or P = 30 - Q/50. Assume the distributor’s costs are zero and you are charging your distributor a single price W per mask.

In this case the price W you charge your distributor is not higher than profit per unit sold.

The price P and the quantity of masks x are:

X is optimal at MR = MC.

MR = TR' = (P*x)' = 30 - x/25,

MC = TC' = 20,

30 - x/25 = 20,

x = 250 units,

P = 30 - 250/50 = 25.

The profits are:

TP = TR - TC = 25*250 - 20*250 = 1250

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