C. Graph the isoquant for Qo = 20 and the isocost line. Label the tangency point E.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter9: Production Functions
Section: Chapter Questions
Problem 9.1P
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I have graphed the isoquant line but I can’t figure out how to graph the isocost line? Could you verify my math and show the isoquant and isocost line graphed please?
3.
Isocost and Isoquant
Consider the production function:
- The prices of inputs L and K are:
The firm's target level of output is:
Q(L, K) = LK
r = 5
w = 4
Qo = 20
calculate the minimum achievable total cost (Cmin) and the cost-minimizing (L*, K*)
combination. Use the tangency condition: MRTSKL = W/r.
(Socost line C wL trk
QLK - 2o → 20-K=O
40
Cmin =
TL 4L+ 5 K = Co
4.L= 20
L* =
=MRTS KL =
mPL
-AK
4
A L
mpK
K* =
c* mine wĽ trk
L.k= 20
R= 4
te the isocost equation for the cost-minimizing isocost line in slope-intercept form:
K =
등 -
L
C. Graph the isoquant for Qo = 20 and the isocost line. Label the tangency point E.
K
a
4.
5
4
10
Qo= 20
13 14
1o r 12
0: 400
Transcribed Image Text:3. Isocost and Isoquant Consider the production function: - The prices of inputs L and K are: The firm's target level of output is: Q(L, K) = LK r = 5 w = 4 Qo = 20 calculate the minimum achievable total cost (Cmin) and the cost-minimizing (L*, K*) combination. Use the tangency condition: MRTSKL = W/r. (Socost line C wL trk QLK - 2o → 20-K=O 40 Cmin = TL 4L+ 5 K = Co 4.L= 20 L* = =MRTS KL = mPL -AK 4 A L mpK K* = c* mine wĽ trk L.k= 20 R= 4 te the isocost equation for the cost-minimizing isocost line in slope-intercept form: K = 등 - L C. Graph the isoquant for Qo = 20 and the isocost line. Label the tangency point E. K a 4. 5 4 10 Qo= 20 13 14 1o r 12 0: 400
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