Let C(Q) denote the total cost of producing Q units of a good. Show that the ave

Question

Let C(Q) denote the total cost of producing Q units of a good. Show that the average cost is minimized at the point where average and marginal costs coincide. Maximize the function f(x, y) = -2x^2 - 7y^2 + xy + 12x + 37y. Suppose the total weekly revenue (in dollars) that a company obtains by selling goods x and v is R(x, y) = -(1/4) x^2 - (3/8) y^2 - (1/4) xy + 300x + 240y Find the profit-maximizing levels of x and y if the total weekly cost attributed to production is C(x, y) = 180x + 140y + 5000 A monopolist has a demand curve P(Q) = kQ^-alpha (0

Explanation / Answer

1)given total cost =C(Q)

marginal cost =C'(Q)

average cost Ca(Q)=(C(Q))/Q

C'a(Q) =[(C'(Q))Q -(C(Q))*1]/Q2

C'a(Q) =[QC'(Q) -C(Q)]/Q2

Average cost is minimised when C'a(Q) =0

[QC'(Q) -C(Q)]/Q2=0

[QC'(Q) -C(Q)]=0

QC'(Q) -C(Q)=0

C(Q)=QC'(Q)

(C(Q))/Q=C'(Q)

AVERAGE COST =MARGINAL COST

so average cost is minimised at the point where average cost and marginal cost coincide

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