Suppose your newspaper is trying to decide between two competing desktop publish

Question

Suppose your newspaper is trying to decide between two competing desktop publishing software packages, Macro Publish and Turbo Publish. You estimate that if you purchase x copies of Macro Publish and y copies of Turbo Publish, your company's daily productivity will be U(x, y) = 4 x^0.9 y^0.1 + x where U(x, y) is measured in pages per day (U is called a utility function.) If x = y = 13, by approximately how many pages per day will productivity increase if x is increased by one unit? a. A productivity increase of approximately 9.17 pages per day. b. A productivity increase of approximately 3.59 pages per day. c. A productivity increase of approximately 4.59 pages per day. d. A productivity decrease of approximately 65.00 pages per day. e. A productivity increase of approximately 69.59 pages per day. 6. Evaluate g(0,1,0) for g(x, y, z) = In(x + y + z)

Explanation / Answer

5)
U(x,y) = 4*x^0.9 * y^0.1 + x
dU(x,y)/dx = 4*0.9*x^(0.9-1) * y^0.1 + 1
                        = 3.6 * x^(-0.1) * y^0.1 + 1

put x = y=13
increase in productivity = 3.6 * x^(-0.1) * y^0.1 + 1
= 3.6 * 13^(-0.1) * 13^0.1 + 1
   = 3.6*0.774*1.292 + 1
    = 4.6

Answer: c

6)
g(x,y,z) = ln (x+y+z)
g(0,1,0) = ln (0+1+0)
                 =ln (1)
                 = 0
Answer: 0

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