Question

B %134 + Görüntü Bayat/Kaçalt Sayfa Ekle Ekle Tablo Grafik Metin Şek Ortam Yorum Ortak Çalış Biçim Belge POINT A Q=1200 0=1000 Bir şey seçilmedi. Biçimlenecek bir nesne veya metin seçin. A) please show the optimal amount of worker and capital in order to produce 1000 units output on the graph B) at that optimal point, at what rate is the firm's willingness to trade away from capital for one more worker at 1000 units of output (Q)? C) Let Q=f(L,K) be the production function. At point A on the graph above, which of the following equalities holds? 1 Fk/PL<FL/PL 1 Fk/PL=FL/PL 1Fk/PLFL/PL Please explain to someone with little mathematical, economic or engineering knowldege, 131 sözcük o

Answer 1

(a) The optimal amount is shown as below.

Q=1200 Q=1000

As cost increases, considering r and w remains the same, the isocost shifts right. The optimal amount to produce Q=1000 would be where the lowest (the most left) isocost touches (is tangent to) the isoquant of Q=1000. This is where the slope of the isocost is equal to the slope of the isoquant Q=1000. The optimal point is shown as point E.

(b) The slope of the isoquant (MRTS) is the amount of capital to trade away for a unit worker, such that the output remains the same. In this case, at the optimal point, the slope of isoquant is equal to the slope of isocost. The isocost would be as , where L is worker, K is capital and C is the cost of production. The slope would be as
- 7Р. ур Р. тр
or
dK Waru
or $\frac{\mathrm{d} K}{\mathrm{d} L} = - \frac{w}{r}$ , meaning that
MRTS =
. For the given values, we have
MRTS = -2
or . Hence, producing Q=1000, the firm would be willing to trade 0.16 of capital (decrease capital by 0.16, and hence the minus sign) for a unit increase in worker.

(c) The correct option would be

• 1.
  V
  

At point A, the slope of the isoquant is steeper than slope of isocost, meaning that the slope of isoquant is more than the slope of isocost. The MRTS would be as
MRTS =
, for F be the production function, and F_L and F_K are the marginal product of worker and capital. For the isocost be
P.L + PKK = 0
(w and r are price of labor and capital), we have the slope of isocost as $\frac{\mathrm{d} K}{\mathrm{d} L} = - \frac{P_L}{P_K}$ . Taking the absolute values of slopes, we have
MRT SI >
(isoquant's slope at point A is more than isocost's slope at A) or $\frac{F_L}{F_K} > \frac{P_L}{P_K}$ or
V
.

The second condition would be where the optimal point of production is, while the third condition would be where the point is on the right side of optimal point of produciton. The graph is as below.

Q=1000 MRTS,