7) Suppose the production function for good ( q ) is given by ( q=K cdot L ) where ( mathrm{K} ) and ( mathrm{L} ) are capital and labor inputs. Consider three statements about this function:
I. The function exhibits constant returns to scale
II. The function exhibits diminishing marginal productivities to all inputs
III. The function has a constant marginal rate of technical substitution
Which of these statements are true?
A) All of them
B) None of them
C) I and II but not III
D) I and III but not II
E) II and III but not I
8) Stanley consumes only white and red wines and his utility function can be described by ( U(R, W)=R^{0.40} cdot W^{0.60} ), where ( mathrm{R} ) is the number of bottles of red wine and ( mathrm{W} ) is the number of bottles of white wine that he consumes per month. Suppose that his income is ( qquad ) and the price of a bottle of red wine ( $ 20 ) and the price of a bottle of white wine is ( $ 15 ). In this case, Stanley will purchase ( qquad ) bottles of red wine and ( qquad ) bottles of white wine per month. Next, suppose that the price of white wine goes down to ( qquad ) per bottle. After the price change, Stanley consumes 40 bottles of white wine.
A) 500 ; 10 ; 20 ; 12
B) 800 ; 16 ; 32 ; 12
C) 800 ; 32 ; 16 ; 12
D) 500 ; 20 ; 10 ; 7.5
E) None of the above
9) Peter consumes goods ( X ) and ( Y ). The price of good ( X ) is ( mathrm{Px} ) and the price of good ( mathrm{Y} ) is Py, Peter's income is I. If both prices increase by ( 50 % ), and Peter's income decreases by ( 50 % ) then the
A) slope of the budget constraint will increase
B) slope of the budget constraint will decrease.
C) budget constraint will be unchanged.
D) budget constraint will shift outward in a parallel fashion.
E) budget constraint will shift inward in a parallel fashion.
10) Suppose the inverse market demand curve is ( p=100-5 Q ). At a price (p) of 20, consumers' surplus equals
A) 500 .
B) 250 .
C) 640 .
D) 80 .
E) None of the above.
