A firm faces the demand curve $ P = 120 - Q $ and has total cost $ TC = 100 + 5Q + 0.5Q^{2} $.

i) Find the profit‑maximising output, price and profit.

ii) If a specific per‑unit tax of $\text{₦}10$ is imposed, determine the new profit‑maximising output, price and profit.

Question

A firm faces the demand curve $ P = 120 - Q $ and has total cost $ TC = 100 + 5Q + 0.5Q^{2} $.

i) Find the profit‑maximising output, price and profit.

ii) If a specific per‑unit tax of $\text{₦}10$ is imposed, determine the new profit‑maximising output, price and profit.

Accepted Answer

Original: Q=38.33, P=₦81.67, Profit=₦2104.17; After tax: Q=35, P=₦85, Profit=₦1737.5

Gce Model Questions Vol1 2018 Economics Question 13