Question

Use a diagram to discuss whether you agree or disagree with the following statement.“When the discount rate is zero, allocating the same amount of resources is always dynamically efficient.”

Answer 1

Dynamic efficiency is a generalization of the static efficiency case. Dynamic efficiency not only considers the magnitude of the benefits and costs (as is the case with static efficiency), but also considers the timing of the benefits and costs.

Criteria and Condition for Dynamic Efficiency

• Criteria - the allocation of resources across n time periods that maximizes the present value of net benefits from the use of the resource.
• Condition - the present value of marginal net benefits from the last unit consumed in each period must be equal.

Discounting

Discounting is the process used to get the present value. The basis for discounting is the time value of money which states a dollar today is worth more than a dollar in the future. Why?

1.Uncertainty - the future is unknown, will you be around to spend the dollar

2. Inflation erodes the buying power of the dollar

3. Utility gained from consuming today versus consuming in the future

4. Investment opportunities - invest today, earn interest, and have more than a dollar to spend in the future.

5. Basic idea is to get the present value of some future payment to be received at time n.

Formula to get the present value of any future payment is PV = FV ( 1 / ( 1 + r) ⁿ ) where r is the discount rate and n is the number of periods in the future the payment is to be received.

The present value of a series of payments is determined by finding the present value of each payment individually and then summing the individual present values. PV = P_o + P₁(1/(1+r)) + P₂(1/(1+r)² + . . . + P_n(1/(1+r)ⁿ where the subscript denotes the time period the payment is received and r the discount rate. Note, the current time period (0) is not discounted.

When the discount rate is zero, allocating the same amount of resources is always dynamically efficient.