A fast food restaurant currently pays $5 per hour for servers and $50 per hour to rent ovens and other kitchen machinery. The restaurant uses seven hours of server time per unit of machinery time. Determine whether the restaurant is minimizing its cost of production when the ratio of marginal products (capital to labor) is 12. If not, what adjustments are called for to improve the efficiency in resource use? The ratio of prices PK/PL= r/w= 50/5=10 and
The capital to labor MPK/MPL= w/r=12
These two ratios are not equal, the restaurant should change inputs. To make the ratios equal the restaurant should use more capital and less labor. This tells us that the capital is 12 times as productive and 10 times more costly.
A competitive firm sells its product at a price of $0.10 per unit. Its total and marginal cost functions are: TC = 5 - 0.5*Q + 0.001*Q2
MC = -0.5 + 0.002*Q, where TC is total cost ($) and Q is output rate (units per time period). (a) Determine the output rate that maximizes profit or minimizes losses in the short-term. R=P*Q=0.10*Q
MC=-0.5+0.002Q=0.10=MR ; 0.002Q=0.6 ; Q=300
(b) If input prices increase and cause the cost functions to become TC = 5 - 0.10*Q + 0.002*Q2
MC = -0.10 + 0.004*Q,
what will the new equilibrium output rate be? Explain what happened to the profit maximizing output rate when input prices were increased. MC = -0.10 + 0.004*Q=0.10=MR ; 0.004Q=0.20 ; Q=50
An increase in input price causes an increase in the firm’s marginal cost. As we can see the production decrease from 300 to 50. A firms profit will be reduced too.
(a) Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of each firm.
QD(P)=6500 - 100*P
6500 – 100*P=1200*P...
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