1.(Capital and the Labour Market, Question with Mathematical) derivations). Consider our 4- quadrant model (for 1 sector only), take everything as standard there, but with the following particular specification : the production function is given by
Y= AKaL1-a , with 0 ≤a≤1
d. Forget anything you have been told about the shape of the MPL as a function of L in class. Suppose in this sector, capital can be rented freely at r such that MPK= r . What does the four- quadrant equilibrium look like in this case? (It’s still the case that p1= MPL, and the MPL is a function of A, K, L).
1.
(Capital and the Labour Market, Question with Mathematical) derivations). Consider our 4- quadrant model (for 1 sector only), take everything as standard there, but with the following particular specification : the production function is given by
Y=AKaL1-a, with 0 ≤a≤1
a. Show graphically the equilibrium in the labour market, taking A, K as fixed and given.
b. Write down the key equation behind each quadrant.
c. Suppose an interest rate change has the following two effects: K goes down (less capital is used in production and the MPL in quadrant- I still takes this now-lower quantity of K as given) and β goes down. What happens to the equilibrium in the labour market, compared to (a)? (Illustrate graphically, if there any shift on the curve please explain).
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