Explanation:

Under Monopoly, the market demand curve faced by the firm is downward sloping. The monopolist is a price-maker and can choose the price and quantity of output it wishes to produce. The monopolist's objective is to maximize its profit, which is the difference between total revenue (TR) and total cost (TC). To maximize profit, the monopolist needs to choose the right level of output where Marginal Revenue (MR) equals Marginal Cost (MC).

The MR curve under monopoly lies between the AR and Y-axis because of the following reasons:

1. Monopolist faces a downward-sloping demand curve: The monopolist's demand curve is downward sloping, which means that it can sell only a given quantity of output at a higher price. The monopolist needs to lower the price to sell more output. This leads to a decline in the price of each additional unit sold.

2. MR is less than price: In a monopoly market, the price of each additional unit sold declines, which means that the MR is less than the price. The monopolist can sell more output only by lowering the price, which reduces the revenue earned on each additional unit sold.

3. Rate of decline of MR is faster than AR: The rate of decline of MR is faster than the rate of decline of AR. This means that for each additional unit sold, the revenue earned by the monopolist declines at a faster rate than the price.

4. MR curve lies between AR and Y-axis: The MR curve is a slope curve that lies between the AR and Y-axis. This means that the monopolist can increase the quantity of output sold only by lowering the price. As the price decreases, the quantity sold increases, which leads to a decline in revenue earned on each additional unit sold.

Conclusion:

In conclusion, the MR curve under monopoly lies between AR and Y-axis because of the downward-sloping demand curve, MR being less than price, faster rate of decline of MR than AR, and the need to lower the price to sell more output. The monopolist's objective is to maximize profit by choosing the output level where MR equals MC.

1) Just half of the rate of decline of AR