A price taking firm makes machine tools Y using labour and capital
according to the following production function
Y = L^(0.25)*K^(0.25).
Labour can be hired at the beginning of everyweek, while capital can be hired at the beginning of every month. It is given that the wage rate= rental capital =10.
Show that the ahort run cost function if 10Y^4/K* and long run cost function is 10Y^2?
I am not getting the short run cost. I did it like this since capital is fixed so the firm has only choice variable is labour
Now i found the demand function for labour as Y=(L*K)^(0.25) then Y^4/K*=L will be the labour demand. Now the cost function is C=wL+vK=10*[Y^4/K*] + 10K*(this is the extra part i am getting.
For long run cost function I differentiated this cost function with repect to capital and set it equal to zero. Then i got K*=Y^2. I then put it in the short run cost fuction and got the long run cost as C=10Y^2.
Please helpe me. I did by the method given in nicholson.
I have some doubts and i will keep putting them. So any kind of help would be aprreciated.
A monopolist has cost function c(y) = y so that its marginal cost is
constant at Re. 1 per unit. It faces the following demand curve
D(p) =100/p,,.p<=20
0.p>20
Find the profit maximizing level of output if the government imposes a
per unit tax of Re. 1 per unit, and also the dead-weight loss from the
tax.
Locked
