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QUESTIONS for written exam in microeconomics. Select the (unique) correct answer
PRODUCTION THEORY -Varian chaps. 18 - 23
1. A competitive firm is using the factors 1 and 2, to produce output y. If the factor price ratio is
(w1 / w2) > 3, the firm is using only factor 2; if (w1 / w2) < 3, the firm is using only factor 1;
finally, if (w1 / w2) = 3 it is indifferent which factor using in production. Indicate which of the
following alternatives is consistent with cost minimization.
a) the production function is Cobb-Douglas.
b) the factors are perfect substitutes and MP = 3MP (MP = marginal productivity of factor i)
1 2 i
c) the factors are perfect substitutes and the MP = (1/3)MP
1 2
d) factors 1 and 2 are perfect complements, in the proportion 3 to 1
e) none of the other answers is correct
2. A firm has production function y = f (x, z) = αx + βz, for y ≥ 0, where y is output, and x, z the
factors of production. This means that returns to scale are:
a) constant
b) decreasing
c) increasing
d) initially increasing, then decreasing
e) none of the other answers is correct
a a
3. Consider the production function: f(x1,x2) = (x1 x2 ), where a is a positive parameter. Indicate
for which values of a the returns to scale in production are increasing:
a) only if a > 2
b) only if a > 1
c) only if a > 1/2
d) it is impossible to answer
e) none of the other answers given is correct
4. A firm has production function y = f (x, z) = (xz) / (x + z), for y ≥ 0, where y is output and x, z
the factors of production. This means that returns to scale are:
a) constant
b) decreasing
c) increasing
d) initially increasing, then decreasing
e) none of the other answers is correct
5. Given the production function: f(x1, x2) = (x1 αx2β), with α and β positive constants, indicate
which values of α and β yield increasing returns to scale , together with decreasing marginal
productivity of factors:
a) for any positive value of α and β
b) α and β lie in the interval (0, ½)
c) α and β lie in the interval (½, 1)
d) α and β lie in the interval (1, 2)
e) none of the other answers is correct, because decreasing marginal productivity is never associated
with increasing returns to scale.
6. A competitive firm has production function y = x11/2x21/4. Factor prices are [1, 1], respectively,
and output price is p = 4. Determine the amount of y maximizing short run profit, when the quantity
of factor 2 is fixed at x2 = 16.
1/2 1/4
7. A competitive firm has production function y = x1 x2 . Factors prices are [1, 1], respectively,
output price is p = 4. Determine the quantity of y maximizing long run profit.
8. A competitive firm has production function: y = 2x1 + 3x2. Factors prices are [1, 3], respectively.
What is the minimum total cost for producing y = 100?
1/2 1/2
9. A firm has production function y = x1 x2 . Factors prices are w1 = 4, w2 = 2, respectively. The
minimum total cost for producing y = 100 is:
10. A firm produces output y with the factors x1 e x2 , according to the production function
y = min {2x1, x2}. Determine the minimum total cost for producing y = 100, when factor prices are
[1, 3].
2
11. Let C (y) be the total cost function of a firm. If C(y) = 144 + 16y . Determine the minimum
average cost.
12. John has a workshop where he repairs cars (a). For all a ≥ 0 his total costs are:
c(a) = 5a2 + 120a + 80. If he repairs 20 cars, his average variable costs will be:
2
13. The total cost function of a competitive firm is c(y) = 2 + (y /3). At what market price the firm
is producing 30 units of y?
14. In a competitive industry, a firm with marginal costs MC, average variable costs AVC, and
average cost AC, chooses the short run output quantity such that:
a) p = MC and p > AC
b) p = MC and p = AVC
c) p = MC and p ≥ AVC
d) p > MC and p > AC
e) none of the other answers given is correct
15. In a competitive industry in the long run, in the absence of incentives for entrance or exit of
firms from the market, each firm with marginal costs MC (y) and average costs AC (y), produces
the quantity y wherein:
a) p = MC and p > AC
b) p = MC and p = AC
c) p = MC and p < AC
d) p > MC and p > AC
e) none of the other answers given is correct
16. In a competitive industry, there is a firm with cost function:
c(0) = 0; c(y) = 16 + 2y2 for y > 0. In the long run, what is the minimum price at which the firm is
prepared to produce a positive output?
17. In a competitive market, there are two firms. Due to the presence of a quasi-fixed factor they
2 2
have long run cost functions c(0) = 0; c(y1) = y1 + 400, if y1 > 0; c(y2) = y + 144, if y2 > 0.
2
Determine the minimum price at which both firms are willing to stay in the market.
18. A good is produced by small firms with the same technology and cost function: c(0) = 0 and
c(y) = 100 + y2. In a long-run equilibrium of the industry, how many firms are producing a positive
output, if the inverse market demand function for Y is p = 820 - 2Y?
s s s
19. A competitive firm has short-run cost function c (0) = F; c (y) = F + c (y), where F = 500
s s v
2
is fixed cost, and c (y) is variable cost. Knowing that c (y) = y + 144, if y > 0, determine the
v v
minimum price at which the firm is willing to produce a positive short run output.
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