Question

Q6. For the cost function C (x) = √(2&x) + x^2/( 900) determine

The cost at the production level 425 units of output=

The average cost at the production level 425 units of output=

The marginal cost at the production level 425 units of output=

Q7. An exporter of Japanese tea estimates that consumers will buy approximately D(p)=2565⁄p^2 pounds of tea per week when the price is p dollars per pound.

A) At what rate will the demand of tea be changing with respect to price $ (p) per pound when the price is $5.00? (Ignore negative sign since negative prices do not have any economic interpretation)

B) It is also estimated that t weeks from now, the price of Japanese’s tea will be p(t)=0.10t^2+0.05t+10 dollars per pound. At what rate will the price for coffee be changing with respect to weeks (t) when it is 9 weeks from now?

Please provide clear answer for both questions with written solutions.

Answer 1

6. Given Cost Function:

C(x) = $\sqrt{2x}$ + x2 / 900

At Production Level of 425 Units,

Cost, C(425) = + 4252 / 900

V2 * 425

   = $ 229.85

Average Cost = C(x) / x = ( $\sqrt{2x}$ + x2 / 900 ) / x

= + X / 900

√2/x

At X = 425,

Average Cost = (2/425)1/2 + 425/900   

= $0.54

Marginal Cost = C' (x) = d C(x) / dx = $\sqrt{2}$ * (1/2$\sqrt{x}$ ) + (2x / 900)

At X = 425, Marginal cost = $0.978

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7A) D(p) = 2565 /p 2

To find rate of change of demand with respect to price when p = $5

Rate of change of demand wrt price = dD/dp = 2565 * -2 p-3

= -5130 / p3

dD / Dp | p =5    = -5130 / 53

   = - 41 Units per dollar

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7 B) Price function, p(t) = 0.1t2 + 0.05t + 10

To find dp/dt when t = 9 weeks

dp/dt = 0.2t + 0.05

At t=9, dp/dt = 0.2*9 + 0.05 = 1.85 dollars / week