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) = 6x0.9y0.4 + x where U(x, y) is measured in pages per day (U is called a utility function). If x = y = 10, calculate the effect of increasing x by one unit. (Round your answers to two decimal places.) pages per day Interpret the result. This means that, if your company now has copies of Macro Publish and copies of Turbo Publish, then the purchase of one additional copy of Macro Publish will result in a productivity increase of approximately

Answer 1

Answer: 11.722

Explanation:

Two competing desktop publishing packages ; Macro publish and Turbo publish

If x and y copies of Macro publish and Turbo publish are purchased respectively ;

Daily Productitvity equals ;

U(x, y) = 6(x^0.9) (y^0.4) + x

where U(x, y) is measured in pages per day U is called a utility function

If x = y = 10

U(x, y) = 6(x^0.9) (y^0.4) + x

Therefore,

U(10,10) = 6(10^0.9) (10^0.4) + 10

U(10,10) = 119.716 + 10 = 129.716

The effect of increasing x by one unit results in

x = 11, y = 10

U(x, y) = 6(x^0.9) (y^0.4) + x

Therefore,

U(11,10) = 6(11^0.9) (10^0.4) + x

U(11,10) = 130.438 + 11 = 141.438

Productivity increase of approximately U(11,10) - U(10,10) = (141.438 - 129.716)

= 11.722 pages