Economics homework help. Suppose we have a production function,

q = K0.25 L0.25 S0.5

where __S__ refers to the seating capacity of a restaurant which in the short run is fixed at S=100.

**a.** What is the demand function for labor, L(q,v,w) and for capital, K(q,v,w)?

**b.** What is the total cost function, C(v,w,q) ?

**c.** What is the supply function, q (P,v,w)?

**d.** What is the profit function, P (P,v,w)?

**e.** What is the demand function for labor, L(P,v,w) and for capital, K(P,v,w)?

**f.** Find the homogeneity degree of profit function in prices?

**g.** Show the profit function is convex in prices?

**h.** Show the profit function is non-decreasing in price and non-increasing in each qi.