Question

a What is the slope of the isocost line when capital is on the vertical axis...

a What is the slope of the isocost line when capital is on the vertical axis and labor on the horizontal axis and r is the cost of capital and w the cost of labor?

  1. What is the slope of an isoquant at every different point on the isoquant curve?
  1. When the isocost and isoquant lines are tangent to each other what is the mathematical expression that shows this tangency?
  1. The equation that shows the equality of the tangent position of the isoquant-isocost point can be rewritten to show the value of marginal output per dollar spent for each input being used. What is this equation?
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Answer #1

Answer a) Equation of isocost line

M=w.L+r.K

where, M= income, w=wage,L=Quantity of labor, r= rental rate, K= Quantity of capital

Slope of isocost line=∆K/∆L

0= w+ r.(∆K/∆L)

∆K/∆L= -(w/r)

Answer b) Slope of isoquant = Marginal rate of technical Substitution or MRTS

MRTS= Marginal product of labor/ Marginal product of capital

MRTS= MPL/MPK

[ MPL= ∆Q/∆L , MPK= ∆Q/∆K]

Answer c) At tangency the slope of isoquant= Slope of isocost line

MRTS= w/r

MPL/MPK= w/r

Answer d) At tangency Slope of isocost line= Slope of isoquant

w/r= MPL/MPK

Rearranging

MPL/w= MPK/r

where (MPL/w) is marginal output per dollar spend on labor

and (MPK/r) is Marginal output per dollar spend on capital

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