Final answer:
The Cobb-Douglas production function Q = 1.75K⁰·½L⁰·½ displays constant returns to scale, as indicated by the sum of the exponents of K and L being equal to one.
Step-by-step explanation:
The Cobb-Douglas production function in question is Q = 1.75K0.5L0.5. Here, Q stands for output, K for capital, and L for labor. To answer the question, we need to understand the properties of the Cobb-Douglas production function, particularly regarding returns to scale and the elasticity of output in response to changes in inputs.
An important property of the Cobb-Douglas production function is related to its exponents for capital and labor. In this case, both K and L have exponents of 0.5. The sum of these exponents (0.5 + 0.5) equals 1, which indicates constant returns to scale. This means that doubling the inputs (both K and L) will double the output.
For the first statement, a one-percent change in L (labor) will, indeed, cause a one-percent change in Q (output) because the exponent of L is 0.5. This number represents the elasticity of output with respect to labor, which measures the percentage change in output resulting from a one-percent change in labor when all other factors are held constant.
The second statement is incorrect because a one-percent change in K (capital) will also result in a one-percent change in output (Q), not two percent. This error likely arises from misunderstanding the production function, wherein the coefficient (1.75) has no bearing on the proportion of change and does not multiply the elasticity.