The graph to the right shows cost and revenue as functions of number of units of

Question

The graph to the right shows cost and revenue as functions of number of units of a product produced and sold. You need to decide which graph is the cost function and which graph is the evenue function. Estimate marginal cost and marginal revenue at 40 units. Label appropriately. C(x)=c(40)-c(30)/10 = 500-390/10 = 11 r (x)=r(40) -R(10) =330-140/10 =19 Estimate the number of units produced and sold where marginal cost and marginal revenue are equal. Estimate the number of units that should be produced and sold in order to generate maximum possible profit. Is profit increasing or decreasing at 40 units produced and sold? Explain your conclusion using marginal cost and marginal revenue. Estimate a production level where average cost and marginal cost are equal.

Explanation / Answer

As per the calculations MC = 11 and MR = 19

Profit = MR-MC
Profit =0 when MR' = MC' i.e. at be point

At x =25 units MR = MC

Maximum profit is attained when R - C is maximum

hence apprxy at x=70 units

Profit = Revenue-cost

At 40 units the difference between revenue and cost is increasing

Hence profit is increasing

(Or mr is increasing more than mc. Hence profit is increasing)

Average cost = cost/no of units

Marginal cost = increase in cost per unit

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C' = C/x when marginal cost = average cost

Or C'/C = 1/x

Integrate to get

ln C = ln x+K

C = Aex

Since X=0 C =A

C = Cex

When x =1 AC = MC

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