Question

1+2 Multiple choice choose best answer 1l If output is described by the production function Y = LaKI-a, then the production function has: (b) diminishing returns to scale (c) increasing returns to scale (d) constant returns to scale (e) None of the above 2. If output is described by the production function Y L°K, with e the production function has: (a) diminishing returns to scale (b) increasing returns to scale (c) constant returns to scale (d) degree of returns to scale that cannot be determined from the information given (e) None of the above 3. Please explain if the following statement is true or false: "If you pay $10,000 Canadian dollars for a used truck for your business, then the aggregate investment of the economy is increasing by $10,000 Canadian dollars." Justify your answer.

Answer 1

1. Ans is d) constant returns to scale

Explanation:

Y(L,K) = L^α K^{1-α​​​​​​​}

To find the returns of scale we multiply both L and K by t and if we get the power of t = 1 then it has constant returns to scale if power of t < 1 so decreasing returns to scale and if power of t > 1 then increasing returns to scale.

Y(t*L, t*K) = (tL)^{α​​​​​​​} (t*K)^{1-α​​​​​​​}

Y(t*L, t*K) = t * L^{α​​​​​​​} K^{1-α​​​​​​​}

Y(t*L, t*K) = t*Y(L,K)

as the power of t = 1, so constant return to scale.

2.

Ans is a) Diminishing return to scale.

Explanation:

It is so because α + β < 1, so the power of t always comes out will be also less than 1 means decreasing returns to scale.

3. False. Because this is a resale. Used goods are not taken into account for calculating GDP because the value of the truck should have been included in the year of its' manufacture.