Camef Records produces records according to the production function: -A-0.1SL me

Question

Camef Records produces records according to the production function: -A-0.1SL met Re if tabor costs 58 and records sell for $20, the optimal quantity of labor is: Enter as a value. 15. For the production function Q-4L + K, returns to scale: a. Is constant. b, Is increasing c. is decreasing d. Can be increasing, decreasing, or constant depending on the values of L and K. un units of 16. if total cost is given by TC output. 49-EQ + Q, then average cost is minimized at Enter as a value. 17. For a market to be efficient, a. consumer surplus producer surplus b. consumer surplus is maximized c. producer surplus is maximized d. total surplus is maximized 18. If demand is P- 50-2Q and supply is P 10+30, what is the value of the Producer Surpl nter as a value.

Explanation / Answer

Ans 17)

For market to be efficient social welfare is to be maximised and that is possible when Consumer surplus and producer surplus will get maximised hence total surplus needs to be maximised if market to be efficient

Ans 18)

Qd=50-2Q and Qs=10+3Q

then At equilibrium we have Qs=Qd

50-2Q=10+3Q

40=5Q

Q*=8 and P*=34

Producer surplus will be calculated along the supply curve by calculating area of triangle with coordinates at When Quantity is 0 & Price(P) when Quantity is 0, Quantity(Q*=8) and Price(P*=34) at equilibrium

PS=1/2(P-P*)(Q*-0)

Producer Surplus=1/2(50-34)(8-0)=1/2(16)(8)=64

Ans 16)

TC=49-8Q+Q^2

We need to find for which Q ATC will get minimised

ATC=49/Q-8+Q

Now We need to differentiate ATC wrt Q and then equalize FOC to 0 we get

d(ATC)/dQ=-49/Q^2+1=0

49/Q^2=1

Q=7

Now lets check whether we can achieve minimum ATC at Q=7

Redifferentiating FOC with respect to Q

2(49)/Q^3>0 ( when SOC is positive term then we have achieved minimisation and vice versa)

Hence Q=7 at which ATC is minimised

Ans 15)

Q(K,L)=4L+K

Now lets increases K and L to @K, @L respectively @>1

Q(@K.@L)=4@K+@L=@(4L+K)=@Q(K,L)>Q(K,L)

Increasing return to scale if Q(@K.@L)=Q(K,L) then Constant return to scale if Q(@K,@L)<Q(K,L) then decreassing return to scale

We have Increasing return to scale here

Ans 14)

We need to maximise profit

Profit=P*Q-Cost=30(4L-0.15L^2)-8L=120L-4.5L^2-8L=112L-4.5L^2

Differentiaitng wrt L we get

d(Profit)/dL=112-9L=0

L=12.44 aprrox.12

If we again differentiate then we have -9<0 hence Profit will be maximised when L=12

Optimal number is 12.44 but labour cant be fractional number hence i am not writing asnwer as 12.44

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