Consider the following function of two choice variables Z = f (x,y) Write down the first order and the second order conditions for a minimum.

economics

Description

1.(i) Consider the following function of two choice variables

Z = f (x,y)

Write down the first order and the second order conditions for a minimum.

(ii) Suppose an individual’s health status Z (measured on a scale of 0 to 10) is a function of two health enhancing drugs x and y (measured as daily dosages) as follows

Z = - x 2 + 2x - y 2 + 4y+ 5

(a) Find fx, fy, fxy, fyx, fxx, fyy

(b) Show that the function has only one stationary point at x = 1 and y = 2 and it is a maximum.

(c) Estimate the value of the health status Z at the point derived at (b)

2. The marginal cost (MC) for producing a certain article in \$ is given by

where q is the quantity of production. Determine constant A, B, C such that

And hence evaluate the total weekly variable costs involved in producing

(i) 10 items per week

(ii) 100 items per week