Question

1. Use a spreadsheet or similar software to produce the graphs for this question. Cut and paste into this document before converting to pdf.

Assume that the production function is

Y = A K^aL ^1-a

and that A   = 5 and L = 14.

1. Assume and that A   = 5 and L = 14. Plot on one graph the value of output (Y) as a function of capital stock (K) for a = 0.1, 0.5 and 0.8. Compare the shapes of the production function. How does the value of a affect this shape?
2. Assume and that A   = 5 and L = 14. Plot on one graph the value of output per capita (y) as a function of capital stock per capita (k) for a = 0.1, 0.5 and 0.8. Compare the shapes of the production function. How does the value of a affect this shape?
3. Assume and that A   = 5 and a = 0.5. Plot on one graph the value of output per capita (y) as a function of capital stock per capita (k) for L = 8, 14 and 20. Compare the shapes of the production function. How does the value of L affect this shape?
4. Assume and that L =14 and a = 0.5. Plot on one graph the value of output per capita (y) as a function of capital stock per capita (k) for A = 2, 5 and 8. Compare the shapes of the production function. How does the value of A affect this shape?
5. Do the same for production functions (e) and (f) from question #1.

Answer 1

Please note that the curves are labels as per the parameters for your reference.

(a) Y as a function of K is shown below for different values of alpha (0.1, 0.5 and 0.8) when A = 5 and L = 14. As the value of alpha increases, the function becomes flatter as observed below.

(b) Output per worker (y) as a function of capital per worker (k) is shown below for different values of alpha (0.1, 0.5 and 0.8) when A = 5 and L = 14. As the value of alpha increases, the function becomes flatter as observed below.

(c) Output per worker (y) as a function of capital per worker (k) is shown below for different values of L (8, 14 and 20) when A = 5 and alpha = 0.5. As the value of labour (L) increases, the function becomes steeper as observed below.

(d) Output per worker (y) as a function of capital per worker (k) is shown below for different values of A (2, 5 and 8) when L = 14 and alpha = 0.5. As the value of labour (A) increases, the function becomes steeper as observed below.

(e) No information on question #1. Leaving this part because of missing information.