Hi, I would really appreciate if someone could help me out on this question! Im not looking to cheat I just want some kind guidance on how to do the question. Ive looked and I honestly don't know!
Given the demand function P = 100 - .005Q a producer must pay $20 per unit in manufacturing costs and also $20 in rent
1. WHat price will maximise the producer's profit? How much profit will the producer earn? What will be the total rent payment earned by the landlord?
2. If the producer and landlord entered into a profit sharing agreement in which the landlord gets 40% of the profit and the producer 60%. What price should the producer set to maximise profit?
3. Will both the landlord and producer prefer the profit sharing agreement or the original agreement? Which agreement will the customer prefer?
4. Given the demand and cost conditions above suppose the royalty payment was 15% of sales revenue to the landlord. Prove there is a conflict between the landlord and producer in that the landlord has an interest in the books price being lower than the price which maximises the producers profit.
Hmmmm.
Your question reads almost exactly like the "economic textbook" question posted by Godfrey on Sunday Oct 15.
However, in Godfrey's question, the producer is a book publisher. He pays a $20 per-book royalty to the book's author. In your question, the producer pays a $20 rent. Rents tend to be fixed costs. Do you really mean a $20 per-unit of output rent (royalty) payment?
If so, see my response to Godfrey.
If not, then your question begs clarification.
I apologize for any confusion caused by the similarity between the question you have and another one posted previously. Let's address the question based on the assumption that the producer pays a fixed rent of $20, rather than a per-unit rent payment.
1. To find the price that maximizes the producer's profit, we need to consider the producer's revenue and costs. The revenue is given by the demand function P = 100 - 0.005Q, where P represents the price and Q represents the quantity. The producer's cost per unit is $20, regardless of the quantity produced.
To determine the quantity that maximizes profit, we need to find the point where marginal revenue (MR) equals marginal cost (MC). Marginal revenue can be calculated as the derivative of the revenue function, which is -0.005. Marginal cost is constant at $20.
Setting MR equal to MC, we have: -0.005 = 20
Solving for Q, we get Q = 4000.
Substituting Q = 4000 into the demand function, we can find the corresponding price: P = 100 - 0.005(4000) = $80.
To calculate the producer's profit, we need to subtract the total cost from the total revenue. The total cost is $20 (rent) + $20 (manufacturing cost) multiplied by the quantity produced: 20Q = 20(4000) = $80,000. The total revenue is the price multiplied by the quantity: 80(4000) = $320,000.
Therefore, the producer's profit is $320,000 - $80,000 = $240,000.
As for the total rent payment earned by the landlord, it is fixed at $20 per unit of output. Since the producer produces 4000 units, the total rent payment earned by the landlord will be 4000 multiplied by $20, which equals $80,000.
2. If the producer and landlord enter into a profit-sharing agreement, where the landlord receives 40% of the profit and the producer receives 60%, we need to adjust the profit calculation accordingly. The producer's share of the profit will be 60% of $240,000, which is $144,000.
To find the price that maximizes profit under this profit-sharing agreement, we follow the same steps as above and solve for Q. Once we have Q, we can find the corresponding price, which will be different from the result in part 1.
3. To determine whether both the landlord and producer prefer the profit-sharing agreement or the original agreement, we need to compare their positions under each scenario. It depends on their individual preferences and their relative bargaining power in negotiating the profit-sharing terms. The customer's preference will depend on factors such as price sensitivity and value perception.
4. If the landlord receives a royalty payment of 15% of the sales revenue instead of a fixed rent, there might be a conflict of interest between the landlord and the producer. The landlord would prefer a lower price that maximizes the producer's profit since it would result in higher sales revenue and a higher royalty payment. On the other hand, the producer would want to set a higher price to maximize their profit. This conflict arises because the interests of the landlord and the producer do not align perfectly in this scenario.